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Math Help - Hexagon around circle

  1. #1
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    Hexagon around circle

    Hello all,

    I've bought an inflatable spa pool that is 1.8m outside diameter. I want to build a hexagonal wooden frame around it to protect the structure. Each side of the hexagon should touch the pool.
    What internal angle should the hexagon have and how long should each side be ?
    Thanks in advance

    Stu
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by stuartadair View Post
    Hello all,

    I've bought an inflatable spa pool that is 1.8m outside diameter. I want to build a hexagonal wooden frame around it to protect the structure. Each side of the hexagon should touch the pool.
    What internal angle should the hexagon have and how long should each side be ?
    Thanks in advance

    Stu
    All internal angles of a hexagon are 120^\circ.
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  3. #3
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    Quote Originally Posted by stuartadair View Post
    Hello all,

    I've bought an inflatable spa pool that is 1.8m outside diameter. I want to build a hexagonal wooden frame around it to protect the structure. Each side of the hexagon should touch the pool.
    What internal angle should the hexagon have and how long should each side be ?
    Thanks in advance

    Stu
    First get the pool diameter.

    Then, a hexagon side length is Dtan30^o
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  4. #4
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    Thanks all for the replies, just to make sure I've got this right...

    • Pool external diameter is 1.8m
    • so using dtan30 would give me
    • 1.8m x 0.577 = 1.03m length of each side.
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by stuartadair View Post
    Thanks all for the replies, just to make sure I've got this right...

    • Pool external diameter is 1.8m
    • so using dtan30 would give me
    • 1.8m x 0.577 = 1.03m length of each side.
    Correct, but I'm sure that a better approximation would be: s=1.0{\color{red}4}m
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